Engineering & Science
Rohsenow Nucleate Pool Boiling Correlation: Wall Superheat ΔT_e Formula
Calculate boiler tube wall superheat ΔT_e = T_wall - T_sat (K) for nucleate pool boiling at heat flux q″ via Warren Rohsenow’s 1952 bubble-agitation correlation.
Why q″ scales with ΔT_e^3 in nucleate boiling—requiring barely 11 K superheat for 200 kW/m^2!
In Warren M. Rohsenow’s landmark 1952 ASME heat-transfer correlation, departing vapor bubbles violently agitate the liquid thermal boundary layer so boiling heat flux q″ grows with the CUBE of excess wall temperature ΔT_e = T_wall - T_sat! Solving explicitly for required wall superheat ΔT_e at design heat flux q″ (W/m^2): ΔT_e = (h_fg / c_p,l) * C_s,f * ((q″ / (μ_l * h_fg)) * SQRT(σ / (g * (ρ_l - ρ_v))))^(1/3) * Pr_l^n_s, where surface-fluid constant C_s,f = 0.013 for water on mechanically polished stainless/copper and Prandtl exponent n_s = 1.0 for water (1.7 for organic fluids)!
Check atmospheric water at 100 °C (h_fg = 2,257,000 J/kg, c_p,l = 4,217 J/(kg·K), μ_l = 0.000282 Pa·s, σ = 0.0589 N/m, ρ_l = 958.4 kg/m^3, ρ_v = 0.598 kg/m^3, Pr_l = 1.75, C_s,f = 0.013, n_s = 1.0): delivering q″ = 200,000 W/m^2 (200 kW/m^2) requires ΔT_e = 11.24 K (T_wall = 111.24 °C); increasing heat flux 2.5× to 500 kW/m^2 raises ΔT_e by only 2.5^(1/3) = 1.357× to 15.26 K!
| Boiler Heat Flux q″ (Water 100 °C, Csf = 0.013) | Required Wall Superheat ΔT_e | Effective Boiling h = q″ / ΔT_e | Regime Check vs CHF |
|---|---|---|---|
| 200,000 W/m^2 (200 kW/m^2 Kettle Reboiler) | 11.24 K | 17,792 W/(m^2·K) | Safe Nucleate Regime (< 1.1 MW/m^2) |
| 500,000 W/m^2 (500 kW/m^2 High-Flux Tube) | 15.26 K | 32,765 W/(m^2·K) | Vigorous Bubble Coalescence |
| Invalid q″ <= 0 or ρ_l <= ρ_v | "Invalid Boiling Inputs" | Error Guard | Positivity Check |
Rohsenow Nucleate Boiling Excess Wall Superheat ΔT_e (K)
Computes ΔT_e = T_wall - T_sat (K) from heat flux q″ (B2, W/m^2), liquid/vapor saturation properties B3:B8, surface-fluid factor C_s,f (B9), and fluid exponent n_s (B10).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= B8, B9 <= 0), "Invalid Boiling Inputs", ROUND((B3 / B4) * B9 * (((B2 / (B5 * B3)) * SQRT(B6 / (9.80665 * (B7 - B8)))) ^ (1 / 3)) * (B10 ^ B11), 2))Effective Nucleate Boiling Heat-Transfer Coefficient h = q″ / ΔT_e (W/(m^2·K))
Divides heat flux B2 by the Rohsenow wall superheat ΔT_e.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= B8, B9 <= 0), "Invalid Boiling Inputs", ROUND(B2 / ((B3 / B4) * B9 * (((B2 / (B5 * B3)) * SQRT(B6 / (9.80665 * (B7 - B8)))) ^ (1 / 3)) * (B10 ^ B11)), 0))Try the example
Use the original values or change them to test your understanding.